Lisa has 10 friends and 34 marbles. What is the minimum number of additional marbles she needs so that she can give each friend at least one marble and no two friends receive the same number of marbles?
Solution: Lisa wants to minimize the number of marbles she gives to her friends without giving any two of them the same number of marbles. The minimum number of marbles she can give to a friend is 1. She then gives 2 marbles to another friend, then 3 to another, then 4, and so on, until the last friend receives 10. The total number of marbles Lisa has given away is $1+2+3+\cdots+10 = \frac{10 \cdot 11}{2}=55$.

Thus, Lisa needs $55-34=\boxed{21}$ more marbles.